Typsetting a variant of division

In Oliver Salazar Celis' "Adaptive Thiele interpolation," ACM Communications of Computer Algebra 56(3), Issue 221, September 2022, page 125 (Eq. 1) we find:

How does one typeset the vertical plus horizontal notation (note that the straight segments touch)?

And what does this notation mean?

• This looks like a continued fraction. May 24 at 18:44
• Google or others give: "an algorithm generates a Thiele-Werner continued fraction representation of the interpolant". May 25 at 8:40

A simple array could do the trick, but I have no idea about what it means. First time I see something like that.

Update: added the array package for better rules connections, as suggested in the comments.

\documentclass{article}
\usepackage{array} % better connections between the rules (see egreg's comment)
\usepackage[textwidth=15cm]{geometry}

\NewDocumentCommand{\myfrac}{mm}{\begin{array}{c|}#1\\\hline\multicolumn{1}{|c}{#2}\end{array}}

\begin{document}
$C_n(x) = \varphi_0[x_0] + \myfrac{x-x_0}{\varphi_1[x_0,x_1]} + \myfrac{x-x_1}{\varphi_2[x_0,x_1,x_2]} + \myfrac{x-x_2}{\cdots} + \myfrac{x-x_{n-1}}{\varphi_n[x_0,\ldots,x_n]},$
\end{document}


• Perfect. Thanks. (accept) Now I'll post on math.SE to see what it means! May 24 at 18:34
• @DavidG.Stork you will need \newcommand not \NewDocumentCommand for mathjax. May 24 at 20:57
• You should also load array in order to improve the connections between the rules. May 25 at 10:08
• @egreg, done!! Thanks for pointing it. May 25 at 10:49

Using holtpolt package.

\documentclass[a4paper,12pt]{article}
\usepackage{holtpolt}
\usepackage{amssymb}

\begin{document}
$C_n(x) = \varphi_0[x_0] +\polter{x-x_0}{\varphi_1[x_0,x_1]}+\polter{x-x_1}{\varphi_2[x_0,x_1,x_2]}+\polter{x-x_2}{\ldots}+\polter{x-x_{n-1}}{\varphi_n[x_0,\ldots,x_n]}$
\end{document}


• Thanks... helpful indeed. May 25 at 17:35